Everything pulls on everything else.

Gravity was not discovered by Isaac Newton Gravity was not discovered by Isaac Newton. What Newton discovered, prompted by a falling apple, was that gravity is a universal force—that it is not unique to Earth, as others of his time assumed.

13.1 The Falling Apple Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree—they are both pulled by Earth’s gravity.

Newton understood the concept of inertia developed earlier by Galileo. 13.1 The Falling Apple Newton understood the concept of inertia developed earlier by Galileo. He knew that without an outside force, moving objects continue to move at constant speed in a straight line. He knew that if an object undergoes a change in speed or direction, then a force is responsible.

13.1 The Falling Apple According to legend, Newton discovered gravity while sitting under an apple tree. He may have been puzzled by the fact that the moon follows circles about Earth. He knew that circular motion is accelerated motion (requires a force). Newton had the insight to see that the moon is falling toward Earth, just as the apple is.

13.2 The Falling Moon The moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.

13.2 The Falling Moon If the moon did not fall, it would follow a straight-line path.

13.3 The Falling Earth Newton’s theory of gravity confirmed the Copernican theory of the solar system.

No longer was Earth considered to be the center of the universe. 13.3 The Falling Earth No longer was Earth considered to be the center of the universe. It became clear that the planets orbit the sun in the same way that the moon orbits Earth. The planets continually “fall” around the sun in closed paths.

13.3 The Falling Earth The tangential velocity of Earth about the sun allows it to fall around the sun rather than directly into it.

13.4 Newton’s Law of Universal Gravitation Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

13.4 Newton’s Law of Universal Gravitation Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object. Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.

13.4 Newton’s Law of Universal Gravitation The force of gravity between objects depends on the distance between their centers of mass.

13.4 Newton’s Law of Universal Gravitation Your weight is less at the top of a mountain because you are farther from the center of Earth.

13.4 Newton’s Law of Universal Gravitation The Universal Gravitational Constant, G The law of universal gravitation can be expressed as an exact equation when a proportionality constant is introduced. The universal gravitational constant, G, in the equation for universal gravitation describes the strength of gravity. G = 6.67 × 10−11 N·m2/kg2)

13.5 Gravity and Distance: The Inverse-Square Law The greater the distance from Earth’s center, the less an object will weigh. An apple that weighs 1 N at Earth’s surface weighs only 0.25 N when located twice as far from Earth’s center. When it is 3 times as far, it weighs only 1/9 as much. But no matter how great the distance, Earth’s gravity does not drop to zero. The gravitational influence of every object, however small or far, is exerted through all space.

13.5 Gravity and Distance: The Inverse-Square Law think! Suppose that an apple at the top of a tree is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity on the apple be only 1/4 as strong? Explain your answer. Answer: No, the twice-as-tall apple tree is not twice as far from Earth’s center. The taller tree would have to have a height equal to the radius of Earth (6370 km) before the weight of the apple would reduce to 1/4 N.

Gravity Near the Earth’s Surface Now we can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth: Solving for g gives: Now, knowing g and the radius of the Earth, the mass of the Earth can be calculated:

Geophysical Applications The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.